In a large bowl, whisk together the eggs, sugar, buttermilk, vanilla extract, and melted butter until smooth. Place a fine mesh sieve over the bowl and add the flour, baking powder, baking soda, cinnamon, and salt. Stir gently to sift the dry ingredients into the wet, then whisk until nearly combined. Add the diced apples and fold them in with a spatula until evenly distributed. Be careful not to overmix the batter. Heat a non-stick skillet or griddle over medium to medium-low heat and add a little clarified butter or a mixture of butter and oil. Once the butter is hot and bubbling, scoop about ¼ cup of batter per pancake into the pan. Optionally cover the pan with a lid to help cook the pancakes through faster. Cook each pancake until bubbles form on top and the bottom is golden brown, then flip and cook until the other side is browned and cooked through. Add a bit of butter to the pan before each new batch. Serve warm with your favorite toppings.